Pressure-Energy Equations of State of the Nucleon
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918485315026944 |
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| author | Liu, Keh-Fei |
| author_facet | Liu, Keh-Fei |
| contents | The pressure-energy equations of state in the nucleon are derived from the gravitational form factors, which parameterize matrix elements of the energy-momentum tensor (EMT), together with EMT conservation. There are two distinct components in the pressure and energy densities. The static pressure distribution arising from the Lorentz trace part of the EMT, as manifested in the spatial stress 1/3 $T^{ii}$, is equal to minus the corresponding trace part of the energy density. This relation may be interpreted as resulting from the depletion of the gluon and quark condensates through the stress-volume relation. This trace-anomaly and sigma-term induced pressure plays a fundamental role in the confinement dynamics of QCD. In contrast, the dynamic pressure distribution from the traceless part of the spatial stress tensor equals 1/d of the corresponding traceless part of the energy density, where d is the spatial dimension. The total pressure is balanced by these two components of the pressure. We point out that the same pressure-energy relations also hold for vortices in type-II superconductors, where the static pressure-energy relation arises from the depletion of the Cooper-pair condensate. Furthermore, these equations of state are identical to those in the $Λ$CDM model of cosmology, where the static pressure-energy relation arises from the cosmological constant. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_04163 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pressure-Energy Equations of State of the Nucleon Liu, Keh-Fei High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory The pressure-energy equations of state in the nucleon are derived from the gravitational form factors, which parameterize matrix elements of the energy-momentum tensor (EMT), together with EMT conservation. There are two distinct components in the pressure and energy densities. The static pressure distribution arising from the Lorentz trace part of the EMT, as manifested in the spatial stress 1/3 $T^{ii}$, is equal to minus the corresponding trace part of the energy density. This relation may be interpreted as resulting from the depletion of the gluon and quark condensates through the stress-volume relation. This trace-anomaly and sigma-term induced pressure plays a fundamental role in the confinement dynamics of QCD. In contrast, the dynamic pressure distribution from the traceless part of the spatial stress tensor equals 1/d of the corresponding traceless part of the energy density, where d is the spatial dimension. The total pressure is balanced by these two components of the pressure. We point out that the same pressure-energy relations also hold for vortices in type-II superconductors, where the static pressure-energy relation arises from the depletion of the Cooper-pair condensate. Furthermore, these equations of state are identical to those in the $Λ$CDM model of cosmology, where the static pressure-energy relation arises from the cosmological constant. |
| title | Pressure-Energy Equations of State of the Nucleon |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.04163 |